Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	275×	body	80	nan
4.0ms	44×	body	1280	valid
3.0ms	45×	body	640	valid
3.0ms	140×	body	80	valid
1.0ms	14×	body	320	valid
0.0ms	13×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

4.0ms	(sqrt (+ x 1.0))
22.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series112.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(sqrt (+ x 1.0))
75.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.1s

Counts

41 → 41

Iterations

Useful iterations: 3 (262.0ms)

Iter	Nodes	Cost
0	84	488
1	183	440
2	498	410
3	1752	402
done	5000	402

prune83.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (+ 0 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
32×	`distribute-lft-out`
28×	`sqrt-prod`
24×	`times-frac`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 80

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
17.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
30.0ms	(/ (+ 0 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series253.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(sqrt (+ x 1.0))
71.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
150.0ms	(/ (+ 0 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify494.0ms

Counts

89 → 89

Iterations

Useful iterations: done (492.0ms)

Iter	Nodes	Cost
0	163	1403
1	386	1139
2	1212	1054
done	5001	1048

prune196.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1.0)))
0.1b	(sqrt (sqrt (+ x 1.0)))
0.1b	(/ (+ 0 1.0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
0.3b	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
63×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
29×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
12×	`times-frac` `distribute-lft-out`
10×	`flip3-+` `associate-r` `associate-l` `flip-+`
9×	`pow-prod-up` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `associate-/l*` `add-log-exp`
3×	`associate-/r*`
2×	`associate-r/` `associate-l/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 167

Calls

4 calls:

5.0ms	(sqrt (sqrt (+ x 1.0)))
5.0ms	(sqrt (sqrt (+ x 1.0)))
34.0ms	(/ (+ 0 1.0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
28.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt (sqrt (+ x 1.0)))
95.0ms	(sqrt (sqrt (+ x 1.0)))
155.0ms	(/ (+ 0 1.0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
32.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify829.0ms

Counts

179 → 179

Iterations

Useful iterations: done (822.0ms)

Iter	Nodes	Cost
0	260	3210
1	567	1921
2	2020	1808
done	5001	1804

prune361.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (fabs (cbrt (+ x 1.0)))) (sqrt (sqrt (+ x 1.0))))
0.2b	(* (* (sqrt (fabs (cbrt (+ x 1.0)))) (sqrt (sqrt (+ x 1.0)))) (sqrt (sqrt (cbrt (+ x 1.0)))))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

40×	`sqrt-prod`
28×	`sqrt-div`
27×	`add-sqr-sqrt`
23×	`-un-lft-identity` `associate-r*`
16×	`pow1`
15×	`add-cube-cbrt`
12×	`cbrt-prod`
11×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-div` `associate-*r/` `pow-prod-down`
9×	`flip3-+` `flip-+`
7×	`associate-l`
6×	`unswap-sqr`
5×	`sqrt-pow1` `pow1/2`
4×	`frac-times` `prod-exp` `cbrt-unprod` `distribute-lft-out` `add-log-exp`
3×	`sqrt-unprod`
2×	`pow1/3` `associate-l/` `-commutative`

Counts

4 → 105

Calls

4 calls:

16.0ms	(* (sqrt (fabs (cbrt (+ x 1.0)))) (sqrt (sqrt (+ x 1.0))))
42.0ms	(* (* (sqrt (fabs (cbrt (+ x 1.0)))) (sqrt (sqrt (+ x 1.0)))) (sqrt (sqrt (cbrt (+ x 1.0)))))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))

series411.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (sqrt (fabs (cbrt (+ x 1.0)))) (sqrt (sqrt (+ x 1.0))))
111.0ms	(* (* (sqrt (fabs (cbrt (+ x 1.0)))) (sqrt (sqrt (+ x 1.0)))) (sqrt (sqrt (cbrt (+ x 1.0)))))
95.0ms	(cbrt (+ x 1.0))
95.0ms	(cbrt (+ x 1.0))

simplify724.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (236.0ms)

Iter	Nodes	Cost
0	267	2439
1	625	2217
2	2100	2071
done	5001	2071

prune505.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: done (1.0ms)

Iter	Nodes	Cost
0	9	11
1	12	11
done	12	9

end0.0ms

sample682.0ms

Algorithm

intervals

Results

149.0ms	1723×	body	1280	valid
143.0ms	7968×	body	80	nan
83.0ms	1228×	body	640	valid
82.0ms	4137×	body	80	valid
34.0ms	606×	body	320	valid
11.0ms	306×	body	160	valid